Question

evaluate the piecewise function at the given values of the independent variable
\\( h(x) = \

$$\begin{cases} \\dfrac{x^2 - 4}{x - 2} & \\text{if } x \ eq 2 \\\\ 8 & \\text{if } x = 2 \\end{cases}$$

(a) \\( h(3) \\) \quad (b) \\( h(0) \\) \quad (c) \\( h(2) \\)

Explanation:

Step1: Evaluate h(3); x≠2

Since $3
eq 2$, use $h(x)=\frac{x^2-4}{x-2}$. First factor numerator:
$x^2-4=(x-2)(x+2)$, so $h(x)=\frac{(x-2)(x+2)}{x-2}=x+2$ (for $x≠2$)
Substitute $x=3$: $h(3)=3+2=5$

Step2: Evaluate h(0); x≠2

Since $0
eq 2$, use simplified $h(x)=x+2$
Substitute $x=0$: $h(0)=0+2=2$

Step3: Evaluate h(2); x=2

Since $x=2$, use $h(x)=8$ directly: $h(2)=8$

Answer:

(a) $h(3)=5$
(b) $h(0)=2$
(c) $h(2)=8$